Continuous Petri nets and transition systems

In many systems, the values of finitely many parameters can be influenced in a continuous way by controls acting with possibly varying strength over intervals of time. For this, we present general models of continuous Petri nets and of continuous transition systems with situation-dependent concurrency. With a suitable concept of morphisms, we obtain a categorial adjunction between these two models, and often even a coreflection. This shows that the concept of regions is also applicable in this continuous setting. Finally, we prove that our categories of continuous Petri nets and of continuous automata with concurrency have products and conditional coproducts.